Method of and apparatus for enlarging/reducing two-dimensional images

ABSTRACT

Method of and apparatus for converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and row direction scales at a high speed, in which use is made of the periodicity of the positional relation between the image elements of the first image arranged in matrix and having various data values and the image elements of the second image arranged in matrix and having various data values to determine, for each one of the second image elements, four second image elements lying on the intersections between two adjacent rows and two adjacent columns in the first image element matrix which rows and columns surround the second image element and constitute a reference from for the second image element, and in which the data value for each second image element is calculated on the basis of the data values of the four first image elements associated with the first image element and the vertical and horizontal coordinates within the reference frame. Both of the above-mentioned periodicity and the coordinates are defined in terms of the ratios between the first and second scales for the first and second two-dimensional images, i.e., magnifications.

This is a division of application Ser. No. 489,350, filed Apr. 28, 1983, now U.S. Pat. No. 4,610,026.

The present invention relates to a method of and apparatus for enlarging/reducing two-dimensional images, and more specifically to a method of and apparatus for converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and row direction scales so that the first image is enlarged or reduced to the second image with magnifications corresponding to ratios between the first scales and the second scales, where the row and column directions in the first image are parallel with those in the second image.

The (first) two-dimensional image to be subjected to enlargement or reduction, i.e., scale conversion is a digital image made of a plurality of image elements (P_(ij)) arranged in matrix (i.e., in i rows and j columns) and having various data values. Similarly, the (second) two-dimensional image resulting from a scale conversion is a digital image made of a plurality of image elements (Q_(mn)) arranged in matrix (i.e., in m rows and n columns) and having various data values.

In this specification, some terms will be defined as follows:

Matrix point . . . An intersection between a row and a column in the above-mentioned matrices. An image element lies on a matrix point.

Original matrix . . . A matrix constituted by the image elements of the (first) two-dimensional image to be subjected to a scale conversion.

Scale-converted matrix or converted matrix . . . A matrix constituted by the image elements of the (second) two-dimensional image resulting from a scale conversion.

Generally, the image scale conversion processing of digital images is carried out through two steps as below:

(1) Determination of positions of scale-converted matrix points in accordance with magnifications of the image scale conversion on the original image matrix (cordinate calculation); and

(2) Calculation of data values representative of saturation levels of the converted matrix points (saturation calculation).

In a conventional image scale converting system, the coordinate calculation and saturation calculation are repetitively carried out sequentially for each individual image elements (matrix points). Reported in a published literature, for example, Preliminary Transactions for 20-th Nation-wide Congress of Information Processing Society of Japan, pp. 73 to 74, 1981 or G. R. Nudd: "Image understanding architechtures", Proc of National Computer Conference, 1980 pp. 377-390 is a hardware for image scale conversion which requires about 1 (one) second for production of outputs representative of 10⁶ image elements. With this apparatus, it takes therefore about 4 seconds for processing a document of A4 size on the assumption that imaging is effected at a density of 8 image elements/nm. Reported in another published literature Study Papers IE76-78/1976 and IE78-12/1978 by The Institute of Electronics and Communication Engineers of Japan is an image scale conversion system based on a microprogram in which the processing speed is of the order of the aforementioned hardware. Also, an approach has been made to simplify the concentration calculation in the image scale conversion. Reported in Japanese Patent Application Laid-Open No. 90375/81 (Laid-open on July 22, 1981) is a system wherein saturation levels calculated in advance for all the combinations of saturation calculation are stored in a memory, and the stored saturation levels are read as desired to determine a saturation level of each individual image element (converted matrix points). According to this system, the saturation calculation can advantageously be effected by referring to a table but repetition of the coordinate calculation must be carried out sequentially in respect of the individual image elements (matrix points).

As described above, the conventional system requires repetition of the coordinate calculation and the saturation calculation in respect of the individual image elements for the sake of image scale conversion and it is unsuitable for high speed processing.

It is an object of the present invention to realize high speed image scale conversion in various types of image scale converting system.

According to one aspect of the present invention, for determination of the positions of the scale-converted matrix points on the original matrix, use is made of periodicity of the positional relation between the original matrix and the scale-converted matrix, the periodicity being defined by mangifications (ratios between the original image scales and the scale-converted image scales).

According to another aspect of the present invention, each rectangular region of the original matrix has its column side and row side divided by r and s, respectively, to define a sub-matrix (r and s being integer large than 1) so that the column direction and row direction magnifications α and β are related with the integers r and s (hereinafter referred to as "a column side division constant" and "a row side division constant"), respectively, as α=r/k_(i) ' and β=s/k_(j) ' (k_(i) ' and k_(j) ' being positive integers), whereby the above-mentioned periodicity of the positional relation is simplified and, at the same time, periodicity of the vertical and horizontal coordinates of the converted matrix points within the rectangular regions of the original matrix each surrounding at least one of the converted matrix points is simplified, and both periodicity thus simplified are used to determine the positions of the converted matrix points on the original matrix. The vertical and horizontal coordinates of the converted matrix points are also defined by the magnifications

In the accompanying drawings useful for describing some preferred embodiments of the present invention:

FIGS. 1A-1C are diagrams for explaining enlargement/reduction of a digital image;

FIG. 2 is a detailed illustrative view of FIG. 1C;

FIG. 3 is a flowchart illustrating a processing sequence for enlargement/reduction of a digital image according to the prior art;

FIG. 4 shows an image scale conversion apparatus according to one embodiment of the present invention and

FIG. 5 is a flowchart illustrating a processing sequence in the apparatus of FIG. 4;

FIG. 6 is an enlarged view of a rectangular region in the original matrix;

FIGS. 7 and 8 are diagrams useful for explaining one aspect of the present invention;

FIG. 9 is a block diagram of another embodiment of the present invention;

FIGS. 10A and 10B illustrate the manner of storing data in the image memory shown in FIG. 9 while

FIG. 11 illustrates transfer of data from the image memory to the input buffer shown in FIG. 9;

FIGS. 12-15 and 17 show examples of the structure of the main portions of the embodiment shown in FIG. 9; and

FIG. 16 is a waveform diagram illustrating clock pulse signals used for shifting original image element data.

Reference will first be made to FIGS. 1A-1C to describe an image scale conversion or an enlargement/reduction of an image. FIG. 1A shows an example of an original digital image, while FIG. 2A exemplarily shows a scale-converted digital image resulting from a magnification of the original image of FIG. 1A with a column direction magnification of 3/2 and a row direction magnification of 3/2. FIG. 1C is a diagram in which the enlarged (scale-converted) image of FIG. 1B is mapped onto the original image of FIG. 1A.

The image enlargement/reduction processing, i.e., the image scale conversion processing means determination of the converted image of Fig. 1B from the original image of FIG. 1A and is carried out through interpolation of the position and data values for the converted matrix points Q₁₁, Q₁₂, . . . , Q₂₁, Q₂₂, . . . , on the basis of the mutual positional relation between the original matrix and the converted matrix and of the data values of the original matrix points P₁₁, P₁₂, . . . , P₂₁, P₂₂, . . . , as illustrated in FIG. 1C.

For a better understanding of the present invention, explanation will now be made on an example of the scale conversion processing according to the prior art with reference to FIGS. 2 and 3.

In FIG. 2 being an enlarged view of FIG. 1C are illustrated an interpolated point or a converted matrix point Q_(mn), an upper-left point P_(X).sbsb.m_(Y).sbsb.n involved in four points of a rectangular region surrounding the interpolated point Q_(mn), a vertical coordinate u_(m) of the interpolated point Q_(mn) within the original image matrix, a horizontal coordinate v_(n) of the interpolated point Q_(mn), lengths A and B of the column direction side and the row direction side of a rectangular region in the original matrix and lengths a and b of the column direction side and the row direction side of a rectangular region in the converted matrix. The lengths A and B are constants specified by the system in question and the lengths a and b are constants specified by magnifications for the scale conversion. A set of information necessary for calculation of the data value representative of the level of saturation for interpolated point or converted matrix point Q_(mn) includes the coordinates u_(m), v_(n) and the data values representative of the levels of saturation for the four original matrix points P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ surrounding the converted matrix point Q_(mn).

Values of u_(m), v_(n), A, B, a and b are discrete since the magnifications for image scale conversion can be limited to rational numbers without causing any inconvenience for practical purposes. On this premise, the values of u_(m), v_(n), A, B, a and b will hereinafter be constructed as integers for simplicity of explanation.

In a conventional image scale converting system, the input information necessary for the interpolation is determined in accordance with proceedings as shown in FIG. 3 (see, for example, Preliminary Transactions for 22nd Nation-wide Congress of Information Processing Society of Japan, pp. 73 to 74, the first term of 1981).

    V.sub.n =Y.sub.n ·B+v.sub.n

    U.sub.m =X.sub.m ·A+u.sub.m

are defined.

In steps 1301, 1302, 1303, 1304, 1305 and 1306, U_(o) =0, u_(m) =U_(m) mod A, X_(m) =U_(m) /A, V_(o) =0, v_(n) =V_(n) mod B, and Y_(n) =V_(n) /B are respectively loaded on an image memory. In step 1307, values for four points P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ near or surrounding the interpolated point Q_(mn) are loaded on the image memory. In step 1308, results from the steps 1302, 1305 and 1307 are used as input information to calculate an interpolation. In step 1309, V_(n+1) =V_(n) +b and n=n+1 are calculated, and in step 1311, U_(m+1) =U_(m) +a and m=m+1 are calculated. In the above procedures, "mod" represents a remainder after division and "/" represents a divisional operation.

It has been proven that in accordance with the above procedures, it takes about 1 (one) second for obtaining a converted image of 10⁶ matrix points. This means that about 4 seconds are required to obtain a converted image of A4 size with a facsimile of 8 scanning lines/nm. Practically, in the above procedures, calculations in the steps 1305 and 1306 can be effected in parallel and calculations in the steps 1307 and 1308 can also be effected in parallel. In the parallel calculations, paths of processing in the steps 1306 and 1307 are dominant in determining the processing time.

In one aspect of the present invention, high speed image scale conversion in various types of systems is achieved by causing paths of steps 1306 and 1307 to be processed at high speeds.

More particularly, the sequences of data representative of the above-mentioned u_(m), v_(n), difference of X_(m+1) -X_(m) and difference of Y_(n+1) -Y_(n) are periodical sequences having respective fundamental cycles of a fixed period, and use is made of the periodicity of these sequences of data to increase the speed of the image scale conversion processing.

In one embodiment, the data of the fundamental cycles are initially loaded on circulating registers and the data in the register are circulatively shifted with timing pulses for taking out necessary data.

The periodicity of the above-mentioned sequences of data may be explained as follows.

The periodicity of v_(n) and u_(m)

As described above, v_(n) =V_(n) mod B and v_(n+1) =V_(n) +b. Thus, for any number n

    v.sub.n+B V.sub.n+B mode B=(V.sub.n +B·b) mod B=V.sub.n mod B=v.sub.n

Accordingly, the sequence of data v_(n) is a periodic sequence having a period of B or smaller and its fundamental cycle consists of v₀, v₁, v₂, . . . , v_(B-1).

Similarly, the sequences of data u_(m) is a periodic sequence having a period of A or smaller and its fundamental cycle consists of u₀, u₁, u₂, . . . , u_(A-1).

Periodicity of (Y_(n+1) -Y_(n)) and (X_(m+1) -X_(m))

As described above, BY_(n) =Y_(n) -v_(n) from this, B(Y_(n+1) -Y_(n))=b-(v_(n+1) -v_(n)). Assuming that Y_(n+1) -Y_(n) =ΔY_(n), for any number n,

    B·ΔY.sub.n+B =b-(v.sub.n+B+1 -v.sub.n+B)=b-(v.sub.n+1 -v.sub.n)=B·ΔY.sub.n

    ∴ΔY.sub.n+B =ΔY.sub.n

Accordingly, the sequence of data ΔY_(n) Y_(n+1) -Y_(n) is a periodic sequence having a period of B or smaller and its fundamental cycle consists of ΔY₀, ΔY₁, ΔY₂, . . . , ΔY_(B-1).

Similarly, the sequence of data ΔX_(m) =X_(m+1) -X_(m) is a periodic sequence having a period of A or smaller and its fundamental cycle consists of ΔX₀, ΔX₁, ΔX₂, . . . , ΔX_(A-1).

Referring now to FIG. 4 showing an overall construction of an image scale converting apparatus according to one embodiment of the present invention, the apparatus comprises a processor 1401 such as a 16 bit microcomputer, a parallel/serial converter (hereinafter referred to as a P/S converter) 1402 for converting image element data of the original image (hereafter referred to as original image element data) read out of a main memory of the processor 1401 in parallel into serial data, a demultiplexer 1403 for selecting input lines to a line buffer memory 1404 which is a shift register for storing the original image element data on a specified number of rows (for example, four rows) in the unit of rows, a multiplexer 1405 for selecting output lines from the buffer memory 1404, an interpolation calculator 1406 which may be, for example, a ROM and receives data values of image elements near or surrounding an interpolated point (i.e., a converted matrix point) from the multiplexer 1405 and data of vertical and horizontal coordinates u_(m) and v_(m) from circulating registers 1413 and 1414 as well and which delivers out a data value representative of the saturation level of an image element of an image subjected to image scale conversion, a serial/parallel converter (hereinafter referred to as S/P converter) 1407 which converts image scale conversion image data delivered out of the interpolation calculator 1406 in series into parallel data and which writes the parallel data into the main memory of the processor 1401, a read/write controller (hereinafter referred to as R/W controller and including, for example, address registers, address calculating ALU and gate circuits) 1408 for controlling data transfer from the processor 1401 to the P/S converter 1402 and data transfer from the S/P converter 1407 to the processor 1401, a shift controller 1409 which receives, from a circulating register 411, shift pulses for determining the number of shiftings to be effected in the buffer memory 1404 and delivers the shift pulses to the buffer memory 1404 and may include, for example, shift pulse counters and gate circuits, and a circulating register 1410 which causes address information in the main memory of the processor 1401 to be delivered sequentially so as to be fetched by the buffer memory 1404 each time one column interpolation is effected. The circulating register 1411 sequentially delivers the shift pulses for determining the number of shiftings in the buffer memory 1404 each time one image element is interpolated. The apparatus further comprises a frequency divider 1412 for counting interpolated image elements for one row, a circulating register 1413 which sequentially delivers a horizontal coordinate v_(n) of an interpolated point or a converted matrix point within an associated rectangular region in the original matrix to the interpolation calculator 1406 each time one image element interpolation is effected, and a circulating register 1414 which sequentially delivers a vertical coordinate u_(m) of the interpolated point or the converted matrix point within the associated rectangular region in the original matrix to the interpolation calculator 1406 each time one row of image element interpolation is effected. When making correspondence of FIG. 4 to symbols of FIG. 2, it is noted that v_(n) corresponds to the output of the circulating register 1413, u_(m) corresponds to the output of the circulating register 1414, Y_(n+1) -Y_(n) =ΔY_(n) corresponds to the output of the circulating register 1411, X_(m+1) -X_(m) =ΔX_(m) corresponds to the output of the circulating register 1410, one pulse resulting from a count-up for n corresponds to the inputs to the registers 1411 and 1413, one pulse resulting from a count-up for m corresponds to the inputs to the registers 1410 and 1414, and the data values for P_(X).sbsb.m_(+1Y).sbsb.n and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ correspond to outputs of the multiplexer 1405. Especially, the buffer memory 1404 comprises a shift register in order to determine image elements near or surrounding the interpolated point on the basis of ΔY_(n).

The operation of this embodiment will be described with reference to FIG. 5. In step 1501, the processor calculates fundamental cycles for the periodic sequences of data v_(n), ΔY_(n), u_(m) and ΔX_(m) on the basis of the magnifications for the image scale conversion, i.e., A/a in the row direction and B/b in the column direction (A and B are specific to the apparatus) and loads these fundamental cycles of data in the circulating registers 1410, 1411, 1413 and 1414. In step 1502, coordinates data of the leading two rows of the original image are loaded on the buffer memory 1404. In step 1503, coordinates of the subsequent two rows of the original image are calculated on the basis of ΔX_(m). In step 1504, the subsequent two rows are loaded on empty lines of the buffer memory 1404 on the basis of the coordinates calculated in the step 1503. In steps 1505 and 1507, contents of the shift register representative of two lines in progress of processing in the buffer memory 1404 is shifted by one bit and two image elements overflowing are fetched into the interpolation calculator 1406. In step 1506, it is judged whether the number of shiftings in the step 1507 reaches the value of ΔY_(m) . In steps 1508 and 1509, v_(n) and ΔY_(n) are respectively subjected to rotate shifting to provide v_(n+1) and ΔY_(n+1), respectively. In step 1510, an interpolation calculation is carried out based on v_(n), u_(m) and data values representative of the saluration levels for new four image elements overflowing from the buffer memory. In step 1511, it is judged whether the interpolation for one row is finished. In steps 1512 and 1513, u_(m) and ΔX_(m) are respectively subjected to rotate shifting to provide u_(m+1) and ΔX_(m+1), respectively. In step 1514, it is judged whether the interpolation for one image is finished.

In this embodiment, particular proceedings in the steps in FIG. 5 are carried out in parallel. To this end, parallel processings are carried out of steps 1506 and 1507, step 1507, step 1508 and step 1509; step 1512 and step 1513, and steps 1503 and 1504 and steps 1505 to 1513. Specifically, the entire processing time for the paths of processing in the steps 1505 to 1513 is equal to the time for shifting a number of image elements of the image subjected to the image scale conversion in the shift register. This means that it takes about 0.6 seconds for obtaining an image scale converted image of A4 size of 8 image elements/mm by means of the shift register of Am 2827 manufactured by Advanced Micro Devices, Inc. On the other hand, the entire processing time for the paths of processing in steps 1503 and 1504 is equal to a product of the number of total bytes in the original and image scale converted images and the transfer speed in the bus. This means that about 1 (one) second is required for obtaining the image scale converted image of A4 size at a transfer speed of 1M bytes/sec in the bus.

As described above, proceedings in the steps 1305, 1306, 1307 and 1309 in FIG. 3 which disfigure the conventional apparatus are replaced by those in steps 1505 to 1509 in FIG. 5 so that the image scale conversion of the A4 size image requiring about four seconds for its completion with the convertional apparatus can advantageously be carried out in about one second with the apparatus according to the embodiment of the present invention.

The periodicity of the positional relation between the original image matrix and the scale converted image matrix as well as the periodicity of the vertical and horizontal coordinates of a converted matrix point within its associated rectangular region in the original matrix may also be explained as follows according to another aspect of the present invention.

As has already been described with reference to FIG. 2, the image scale conversion is a processing of converting a first image {P_(ij) } into a second image {Q_(mn) }. Some symbols and terms will be further defined herein. An original image element in the original matrix which is coincident with or in close proximity of an image element Q_(mn) in the converted matrix is represented by P_(X).sbsb.m_(Y).sbsb.n (see FIG. 6). Thus, the image element or a converted matrix point Q_(mn) exists within a rectangular region defined by four points P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁, and this region is termed a referrence frame for Q_(mn) and represented by a symbol C_(mn). The vertical and horizontal coordinates of an image element Q_(mn) within its associated reference frame C_(mn) are represented by u_(m) and v_(n), respectively. The symbols (X_(m), Y_(n)) and (u_(m), v_(n)) are termed as intermatrix vertical and horizontal coordinates and intramatrix vertical and horizontal coordinates of an image element Q_(mn) at its associated converted matrix point.

    X.sub.m =[{(m-1)×a}/A]+1                             (1)

    Y.sub.n =[{(n-1)×b}/B]+1                             (2)

    u.sub.m ={(m-1)}∥A                                (3)

    v.sub.n ={(n-1)}∥B                                (4)

where symbols "[ ]", "/" and "∥" denote Gauss' notation, divisional operation and remainder after division, respectively. And ΔX_(m) ≡X_(m+1) -X_(m) and ΔY_(n) ≡Y_(n+1) -Y_(n), as already mentioned.

Since, on the other hand, the relation of a=A/α and b=B/β stands by letting α and β be magnifications in the column direction and row direction, each of the X_(m), Y_(n), u_(m) and v_(n) can be expressed as a function of the magnifications α and β by applying the above relations to equations (1) to (4).

Referring now to FIG. 6, each rectangular region in the original matrix, i.e., each reference frame has its column direction side divided by r dividing lines (r being an integer not less than 2) and its row direction side divided by s dividing lines (s being an integer not less than 2), as shown by dotted lines. The integer numbers r and s are column side and row side division factors, respectively. In the second aspect of the present invention, an image element Q_(mn) of the converted image can lie only on an intersection between the longitudinal and lateral dividing lines in a reference frame. In other words, α, β, r and s should be determined such that the following conditions be met:

    u.sub.m =(A/r)×k.sub.i =u.sub.r ·k.sub.i    (5)

    v.sub.n =(B/s)×k.sub.j =u.sub.s ·k.sub.j    (6)

    a=(A/r)×k.sub.i '=u.sub.r ·k.sub.i '        (7)

    b=(B/s)×k.sub.j '=u.sub.s ·k.sub.j '        (8).

where k_(i), k_(j), k_(i) ' are positive integers. Then,

    u.sub.m+kr =u.sub.m                                        (9)

    v.sub.n+ks =v.sub.n                                        (10)

    ΔX.sub.m+kr =ΔX.sub.m                          (11)

    ΔY.sub.n+ks =ΔY.sub.n                          (12)

are held, where k is an optional integer. That is, u_(m), v_(n), ΔX_(m) and ΔY_(n) constitute respective periodic sequences of data.

Equations (9) to (12) will be proven hereunder.

Proof of Equations (9) and (10) From equations (3) and (7), ##EQU1##

Similarly, it can be proved that v_(n+ks) =v_(n).

Proof of Equations (11) and (12)

The spacing between the first row of the original matrix and the (m+kr+1)th row of the converted matrix will be

    A·X.sub.m+kr+1 +u.sub.m+kr+1 =A·X.sub.m+kr +u.sub.m+kr +a

    ∴A·(X.sub.m+kr+1 -X.sub.m+kr)=a-(u.sub.m+kr+1 -u.sub.m+kr).

On the other hand, from equation (9)

    U.sub.m+kr+1 =u.sub.m+1 and u.sub.m+kr =u.sub.m

From the above definition,

    X.sub.m+kr+1 -X.sub.m+kr =ΔX.sub.m+kr

    ∴A×ΔX.sub.m+kr =a-(u.sub.m+1 -u.sub.m) (13).

On the other hand, the specing between the first row of the original matrix and the (m+1)th row of the converted matrix will be

    A·X.sub.m+1 +u.sub.m+1 =A·X.sub.m +u.sub.m +a

    ∴A·(X.sub.m+1 -X.sub.m)=a-(u.sub.m+1 -u.sub.m)

    so that,

    A·ΔX.sub.m =a-(u.sub.m+1 -u.sub.m)          (14).

From equations (13) and (14),

    ΔX.sub.m+kr =ΔX.sub.m

can be obtained. Similarly, it can be proved that ΔY_(n+ks) =ΔY_(n).

Equations (9) to (12) as above show that u_(m), v_(n), ΔX_(m) and ΔY_(n) have periodicity. Specifically, u_(m) and ΔX_(m) are cyclic with a period of r or r divided by a positive integer and v_(n) and ΔY_(n) are cyclic with a period of s or s divided by a positive integer. In the second aspect of the present invention use is made of the periodicity purposely to raise the speed of the image scale conversion processing in the following manner, as shown in FIG. 7.

(1) Since data u_(m), v_(n), ΔX_(m), and ΔY_(n) have periodicity, their periodical sequences data, namely, calculated values of {u₁, u₂, . . . , u_(r) }, {v₁, v₂, . . . , v_(s) }, {ΔX₁, ΔX₂, . . . , ΔX_(r) }, and {ΔY₁, ΔY₂, . . . , ΔY_(s) } are stored in tables 7-10 and referred to repetitively. Thus, there is no need to effect the coordinate calculation for all the image elements in contrast to the conventional apparatus but the same number of values for u_(m) and ΔX_(m) as r and the same number of values for v_(n) and ΔY_(n) as s (for example r=s=16) are calculated at the start of the image scale conversion processing and in the subsequent processing, results of the calculation can simply be referred to, thereby simplifying the method of and the apparatus for the seal conversion and making it possible to raise the processing speed.

(2) Saturation calculation is performed symultaneously for image elements of the converted image on m-th row {Q_(m1), Q_(m2), Q_(m3), . . . }, for image elements of the converted image on (m+L)th row {Q_(m+L1), Q_(m+L2), Q_(m+L3), . . . }, for image elements of the converted image on (m+2L)th row {Q_(m+2L1), Q_(m+2L2), Q_(m+2L3), . . . }, . . . , i.e., for image elements of the converted image on those rows which are spaced by k·L rows vertically from m-th row (k being a positive integer). This is parallel processing for the image scale conversion. The spacing L is a constant which is an integer multiple of r. As will be seen from equations (9) to (12), the individual converted image elements vertically spaced apart from each other at the spacing L have the same intra-matrix coordinates (vertical and horizontal coordinates) and the same difference in column (row) number between two corresponding image elements in the two adjacent reference frames in the row (column) direction. Accordingly, accessing of the original image element data to staturation calculating units can be controlled in common.

The operational principle for the processing generally described hereinbefore will be explained with reference to FIG. 7, Illustrated in FIG. 7 are saturation calculators 1 to 4 which are adapted to process in parallel the individual image elements spaced apart from each other vertically at the spacing L, where L is a constant which is an integer multiple of r (L=kr). The number of the saturation calculators can be selected to conform to a desired degree of parallel processing, with one example being four as shown in FIG. 7. The image data values as a result of image scale conversion are sequentially delivered out of each of the saturation calculators 1, 2, 3 and 4 in the order as shown in FIG. 8. Thus, in FIG. 7, original image element data 5 are converted into scale-converted image element data 6. As well known in the art, data necessary for calculating data representative of the saturation level of a point Q_(mn) in the converted matrix are saturation levels of four original image elements P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb. m_(+1Y).sbsb.n₊₁ which define a reference frame C_(mn) for the original matrix point Q_(mn), and intra-matrix coordinates (u_(m), v_(n)) of the converted matrix point Q_(mn) within the reference frame C_(mn). The manner of calculating the saturation for the matrix point Q_(mn) on the basis of the data as above involves known logical sum method, logical product/sum method, nearest neighbour method and projection method (for example, Preliminary Transactions for Image Engineering Conference, pp. 71 to 74, December 1981) and will no be detailed herein. Of the data necessary for calculating the saturation, the intramatrix coordinates are obtained by referring to tables 7 and 8 as shown in FIG. 7. Specifically, data values of the fundamental cycles for the intra-matrix coordinates {u₁, u₂, . . . , u_(r) } and {v₁, v₂, . . . , v_(s) } are stored in the tables 7 and 8, respectively. Data values of the fundamental cycles for the differences in the column number and in the row number of corresponding matrix points in the adjacent reference frames, i.e., {ΔX₁, ΔX₂, . . . , ΔX_(r) } and {ΔY₁, ΔY₂, . . . , ΔY_(s) } are stored in tables 9 and 10, respectively. Data values for the four original image elements P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb. m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ in the original matrix necessary for calculating the saturation for the converted matrix point Q_(mn) are read out of the original image 5 by making reference to the contents of the tables 9 and 10 and fed to the saturation calculators 1 to 4. The saturation calculator 1 calculates data representative of the saturation levels for converted matrix points Q_(m1), Q_(m2), Q_(m3), . . . . on the m-th row (m=1, 2, 3 . . . ), and original image element data for this purpose exist on X_(m) -th and (X_(m+1))-th rows of the original image. Similarly, other saturation calculators 2 to 4 are supplied with data for two rows from the original image. As shown in FIG. 8, accessing the original image data 5 and execution controlling for the saturation calculators 1 to 4 are carried out by referencing the tables 7 to 10 whose contents have been calculated and stored at the start of the image scale conversion processing. In the subsequent processing procedure the calculation results are referenced repetitively. Data values {u₁, u₂, . . . , u_(r) }, {v₁, v₂, . . . , v_(s) }, {ΔX₁, ΔX₂, . . . , ΔX_(r) } and {ΔY₁, ΔY₂, . . . , ΔY_(s) } are calculated pursuant to equations (1) to (4) on the assumption that the magnifications for the image scale conversion (α times in the column direction and β times in the row direction) are given and known.

As described previously, it is established that the converted matrix point Q_(mn) comes into existence only on intersections of r×s dividing lines on the rectangular region in the original matrix. This establishment may limit the magnifications for the image scale conversion in one sense. By letting the magnifications in the vertical direction be α, a=A/α is held. On the other hand, the above establishment causes such a requirement that a=(A/r)·k_(i) '=u_(r) ·k_(i) ' must be satisfied. From these equations, α=r/k_(i) ' is introduced (r≧2, k_(i) '≧1). Thus, the magnification α is not continuous but is allowed to have discrete values which satisfy the last mentioned equation. For r=16, for example, an allowable value of the magnification α is limited to any one of 16, 8, . . . , 2.0, 1.78, 1.60, 1.45, 1.33, 1.23, 1.14, 1.07, 1.0, 0.94, 0.89, 0.84, 0.80, 0.76 . . . The requirement for the magnification will be put aside practically by setting the column side division factor r appropriately. The magnification β in the row direction can be treated similarly.

Assuming that r=16, α=r/k_(i) '=16/20=0.8, values of u_(m), X_(m) and ΔX_(m) can be calculated from equations (1) and (3) in consideration of a=A/α and ΔX_(m) =X_(m+1) -X_(m) to provide results as shown in Table 1. As will be told from Table 1, each of the ΔX_(m) and u_(m) is a periodic function (period≦r) of m. Values of v_(n), Y_(n) and ΔY_(n) can be calculated similarly but they will not be exemplified herein.

                  TABLE 1                                                          ______________________________________                                         m       X.sub.m       ΔX.sub.m                                                                        u.sub.m                                           ______________________________________                                         1       1             1      0                                                 2       2             1      (1/4) A                                           3       3             1      (1/2) A                                           4       4             2      (3/4) A                                           5       6             1      0                                                 6       7             1      (1/4) A                                           7       8             1      (1/2) A                                           8       9             2      (3/4) A                                           9       11            1      0                                                 10      12            1      (1/4) A                                           11      13            1      (1/2) A                                           12      14            2      (3/4) A                                           13      16            1      0                                                 14      17            1      (1/4) A                                           15      18            1      (1/2) A                                           16      19            2      (3/4) A                                           .       .             .      .                                                 .       .             .      .                                                 .       .             .      .                                                 ______________________________________                                    

Another embodiment of the present invention will now be described. FIG. 9 shows the overall structure of an image seale converting apparatus.

Illustrated in FIG. 9 are an image memory 51, a processor 52 such as a 16-bit microprocessor (e.g., microprocessor 8086 manufactured by Intel), a main memory 53 for storing therein programs for the processor 52, column and row division constants r and s and others, a system controller 54, an input controller 55, a shift controller 56, an output controller 57, input buffers 58 to 61 as designated by IB₁₁, IB₁₂, IB₁₃ and IB₁₄, respectively, saturation calculators or processing elements 62 and 63 as designated by PE₁ and PE₂, respectively, and output buffers 64 and 65 as designated by OB₁ and OB₂, respectively. Principal signal lines in FIG. 9 are a common bus 101, a system start (SYS-START) signal line 102, a system end signal (SYS-END) line 103, a data input start signal (IN-START) line 104, a data input end signal (IN-END) line 105, a load signal (PS-LOAD) line 106 connected to parallel/serial (PS) registers included in the processing elements, a signal (PS-EMPT) line 107 for transmission of PS-EMPT representative of data empty in the PS registers included in the processing elements, a start signal (SHIFT-START) line 108 connected to the shift controller 56, a signal (SP-FULL) line 109 for transmission of SP-FULL representative of full data conditions in serial/parallel (SP) registers included in the processing elements, a load signal (OB-LOAD) line 110 connected to the output buffers 64 and 65, a data output start signal (OUT-START) line 111, a data output end signal (OUT-END) line 112, a data processing end signal (DONE) line 113, a line 114 for transmission of a clock φ₁, a line 115 for transmission of clock φ₂, a line 116 for transmission of vertical coordinate (RA) of intra-matrix coordinates, a line 117 for transmission of horizontal coordinate (CA) of the intra-matrix coordinates, a line 118 for transmission of a clock φ₃, an output buffer enable signal (OB-EN) line 119 connected to the output buffers 64 and 65, and an input buffer load enable signal (IB-EN) line 120 connected to the input buffers 58 to 61. In the following description, signals are denoted by reference numerals representative of corresponding signal lines.

In operation, an original image data values stored in the image memory 51 are sent to the saturation calculators or processing elements 62 and 63 via the input buffers 58 to 61, and the image data are subjected to an image scale conversion and the resulting scale-converted image element data are transferred to the image memory 51 via the output buffers 64 and 65. In this processing, the data transfer from the image memory 51 to the input buffers 58 to 61 is controlled by input controller 55, and the saturation calculators (processing elements) 62 and 63 are controlled by the shift controller 56. The transfer of the converted image element data as a result of the image scale conversion from the saturation calculators (processing elements) 62 and 63 to the image memory 51 via the output buffers 64 and 65 is controlled by the output controller 57. The system controller 54 manages or supervises the input controller 55, shift controller 56 and output controller 57. The saturation calculators 62 and 63 operate in parallel. In FIG. 9, two saturation calculators or processing elements are provided for simplicity of explanation but generally, the number of processing elements is determined in accordance with the degree of parallel processing desired. It is needless to say that a single saturation calculator may be provided.

As shown in FIGS. 10A and 10B, the data for image elements (original image elements and scale converted image elements) are stored in the unit of words each consisting of W bits in the image memory 51. Data representative of a leading image element in each row, i.e., P_(i1) or Q_(m1) is stored at 2⁰ bit of the image memory, where i=1, 2, 3, . . . and m=1, 2, 3, . . . The data transfer from the image memory 51 to the input buffers 58 to 61, that from the input buffers 58 to 61 to the saturation calculators 62 and 63, that from the saturation calculators 62 and 63 to the output buffers 64 and 65, and that from the output buffers 64 and 65 to the image memory 51 are all effected in the unit of words. Therefore, the input buffers 58 to 61 and output buffers 64 and 65 have each a capacity of one word of W bits. One word may consist of 8 bits or 16 bits, for example.

In the saturation calculator 62, the calculation is carried out in the order of Q₁₁, Q₁₂, Q₁₃, . . . , Q₂₁, Q₂₂, Q₂₃, . . . , Q₃₁, Q₃₂, Q₃₃, . . . as shown in FIG. 8. In parallel therewith, the calculation proceeds, in the saturation calculator 63, in the order of Q_(1+L1), Q_(1+L2), Q_(1+L3), . . . , Q_(2+L1), Q_(2+L3), . . . Q_(3+L1), Q_(3+L2), Q_(3+L3), . . . For saturation calculation of a desired image element Q_(mn) of the converted image, data values representative of the saturation levels for four original image elements P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n+1 and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ are required. These four points are present on the X_(m) -th row and the (X_(m) +1)-th row of the original image matrix. In the arrangement of FIG. 9, the input buffers 58 and 59 fetch from the image memory 51 data values of the original image elements in respect of the X_(m) -th row and the (X_(m) +1)-th row, respectively, so as to supply the data to the saturation calculator 62. Similarly, the input buffers 60 and 61 fetch from the image memory 51 data values of the original image elements in respect of the (X_(m) +1)-th row and the (X_(m) +L+1)-th row, respectively, so as to supply the data to the saturation calculator 63. The input buffers 58 to 61 have each a capacity of one word of W bits and read the original image element data in the order as shown in FIG. 11.

The input controller 55 functions to control the transfer of the original image element data from the image memory 51 to the input buffers 58 to 61 and has a construction as shown in FIG. 12. The input controller 55 is started by a data input start signal (IN-START) 104 fed from the system controller 54 and it reads the original image element data from the image memory 51 word by word, sequentially writes the data into the input buffers 58 to 61 and thereafter sends a data input end signal (IN-END) 105 to the system controller 54. Namely, the IN-START signal 104 sets a flip-flop circuit (FF) 201. In the figure, mark "." designates initial states of flip-flop circuits. An output signal of the FF 201 is sent to an AND gate 203 via an OR gate 202, and a data transfer request signal (DREQ) 253 is sent to a direct memory access (DMA) timing controller 233 in synchronism with timings of a fundamental clock signal (CLK) 251. The DREQ 253 also resets the FF 201 and a FF 205. The DMA timing controller 233 controls the bus request in the direct memory accessing. The operational principle of the controller 233 is well known in the art and will not be described herein. When receiving the DREQ 253, the DMA timing controller 233 issues a bus request signal (BREQ) 255 to the processor 52. The DMA timing controller 233 then receives from the processor 52 a confirmation signal (BACK) 254 responsive to the BREQ 255 and issues a data transfer confirmation signal (DACK) 257. The FF 205 is again reset by the DACK 257 sent via an AND gate 209 so that a DREQ 253 is again issued though a route of the OR gate 202 and AND gate 203. A counter 208 is adapted to count the number of issuance of the DREQ 253. When the issue number coincides with the number of the input buffers 58 to 61 (four in this embodiment), the output of the counter 208 sets a FF 207 to enable the AND gate 209. As a result, an IN-END 105 is produced from an AND gate 204 in synchronism with the CLK 251. The IN-END 105 resets the FF 207. In this manner, upon receipt of the IN-START 104, the input controller 55 repeats the issuance of the DREQ 253 which coincides in number with the input buffers 58 to 61. At this time, an address of image element data read out of the image memory 51 is represented by an ADDR 259. The address of the image memory 51 is a two-dimensional address consisting of Y addresses (column addresses) and X addresses (row addresses). Contents of a Y address register 206 are used as a Y address and contents of X address registers 217 to 220 are selected by gates 223 to 226 to provide an X address. The X and Y addresses are latched in a latch 227 in response to an address strobe signal (ASTRB) 260 to control delivery of the ADDR 259. As has already been described with reference to FIG. 11, the original image element data supplied to the input buffers 58 to 61 begin with data on the X₁ -th row, (X₁ +1)-th row, (X₁ +L)-th row and (X₁ +L+1)-th row, respectively. Correspondingly, the X address registers 217 to 220 are set in advance with initial values representative of row numbers X₁, X₁ +1, X₁ +L and X₁ +L+1. The Y address register 206 is initialized to zero. As described previously, upon receipt of the IN-START 104 from the system controller 54, the input controller 55 repeats the issuance of the DREQ 253 which coincides in number with the input buffers 58 to 61. With an initial DREQ 253 issued, the contents of the X address register 217 (XA₁₁) is sent to the latch 227 via the gate 223. Subsequently, the contents of the X address register 218 (XA₁₂), the contents of the X address register 219 (XA₂₁) and the contents of the X address register 220 (AX₂₂) are sequentially sent to the latch 227 in response to second, third and fourth issuances of the DREQ 253. Thus, a shift register 232 is adapted to produce gate control signals which control the gates 223 to 226 so that the X adders registers 217 to 220 are sequentially selected in a manner described above. The gate control signals from the shift register 232 also control AND gates 228 to 231, and load enable signals (IB-LE₁₁ to IB-LE₂₂) 120-1 to 120-4 are sequentially sent to the input buffers 58 to 61 in synchronism with a data strobe signal (DSTRB) 265. Consequently, each of the input buffers 58 to 61 is stored with the original image data read out of the image memory 51 one word by one word in sequence as shown in Table 2.

                  TABLE 2                                                          ______________________________________                                         Order of issuance                                                              of DREQ/DACK    1      2        3    4                                         ______________________________________                                         Selected X address                                                                             XA.sub.11                                                                             XA.sub.12                                                                               XA.sub.21                                                                           XA.sub.22                                 register                                                                       Selected input  IB.sub.11                                                                             IB.sub.12                                                                               IB.sub.21                                                                           IB.sub.22                                 buffer                                                                         ______________________________________                                    

The contents of the Y address register 206 is incremented by +1 each time the IN-END 105 is issued when the data transfer to each of the input buffers 58 to 61 ends. A register 222 is adapted to store the row length (the length of one row) of the original image in terms of words. A comparator 221 is adapted to compare the contents of the Y address register 206 and the register 222. Upon coincidence, a coincidence signal 258 is produced from the comparator 221 to reset the Y address register 206. Concurrently, the contents of each of the X address registers 217 to 220 is added with a value read out of a ΔX register 212 and a resultant sum is set to each of the X address registers 217 to 220. The ΔX register 212 is thus a circulating register for storing the fundamental cycle for the periodic sequences of data being representative of differences between a row number X_(m) of one original matrix point in the reference frame C_(mn) for a converted matrix point Q_(mn) and a row number X_(m+1) of one original matrix point in the reference frame C_(m+1n) for a converted matrix point Q_(m+1n), {ΔX₁, ΔX₂, . . . ΔX_(r) }. Initially, the ΔX register 212 stores the difference in an orderly manner of {ΔX₁, ΔX₂, . . . , ΔX_(r) } and the heading data ΔX₁ is sent to adders 213 to 216. The coincidence signal 258 updates the contents of the X address registers 217 to 220 and at the same time sets a FF 210. When the FF 210 is set, a shift pulse is sent to the register 212 via an AND gate 211 so that the contents of the register 212 changes to {ΔX₂, ΔX₃, . . . , ΔX_(r), ΔX₁ }. Subsequently, each time the comparator 221 detects coincidence of the contents of the Y address register 206 with the contents of the register 222, the contents of the register 212 is shifted sequentially and circulatively. The input controller 55 operates in a manner described thus far.

The output controller 57 functions to control the transfer of the image element data subjected to image scale conversion from the output buffers 64 and 65 to the image memory 51, and has a construction as shown in FIG. 13. The output controller 57 is started by a data output start signal (OUT-START) 111 fed from the system controller 54. When the data transfer from the output buffers 64 and 65 to the image memory 51 ends, the output controller 57 sends a data output end signal (OUT-END) 112 to the system controller 54. The received OUT-START 111 sets a FF 301. An output of the FF 301 is sent to an AND gate 303 via an OR gate 302, and a data transfer request signal (DREQ) 353 is sent to a DMA timing controller 317 in synchronism with timings of a fundamental clock signal (CLK) 351. The DREQ 353 also resets the FF 301 and a FF 304. When receiving the DREQ 353, the DMA timing controller 317 issues a bus request signal (BREQ) 355 to the processor 52. The DMA timing controller 317 then receives from the processor 52 a confirmation signal (BACK) 354 responsive to the BREQ 355 and issues a data transfer confirmation signal (DACK) 356. The FF 304 is again set by the DACK 356 fed via an AND gate 308 so that a DREQ 353 is again issued through a route of the OR gate 302 and AND gate 303. A counter 307 is adapted to count the number of issuance of the DREQ 353. When the issue number coincides with the number of the output buffers 64 and 65 (two in this embodiment), the output of the counter 307 sets a FF 306 to enable the AND gate 308. As a result, an OUT-END 112 is produced from an AND gate 305 in synchronism with the CLK 351. The OUT-END 112 resets the FF 306. In this manner upon receipt of the OUT-START 111, the output controller 57 repeats the issuance of the DREQ 353 which coincides in number with the output buffers 64 and 65. At this time, an address for writing the image memory 51 is represented by an ADDR 358. The address of the image memory 51 consists of Y addresses (column addresses) and X addresses (row addresses). Contents of a Y address register 309 is used as a Y address and contents of X address registers 313 and 314 are selected by gates 315 and 316 to provide an X address. The X and Y addresses are latched in a latch 318 in response to an address stroke signal (ASTRB) 359 to control delivery of the ADDR 318. The image element data subject to image scale conversion is stored in the image memory 51 as described with reference to FIG. 10B. Initial values corresponding to the storage in the image memory are set in advance in the X address registers 313 and 314. The Y address register 309 is initialized to a heading address for storage of the image element data subject to image scale conversion. Upon receipt of the OUT-START 111, the output controller 57 repeats the issuance of the DREQ 353 which coincided in number with the output buffers 64 and 65. With an initial DREQ 353 issued, the contents of the X address register 313 (XA₁) is sent to the latch 318 via the gate 315. With a second DREQ 353 issued, the contents of the X address register 314 (XA₂) is sent to the latch 318 via the gate 316. Thus, a shift register 321 is adapted to produce gate control signals which control the gates 315 and 316 so that the X address registers 313 and 314 are sequentially selected in a manner described above. The gate control signals also control AND gates 319 and 320, and output enable signals (OB-EN₁ and OB-EN₂) 119-1 and 119-2 are sequentially sent to the output buffers 64 and 65 in synchronism with a data strobe signal (DSTRB) 362. Consequently, the data read out of each of the output buffers 64 and 65 is stored in the image memory 51 one word by one word. The contents of the Y address register 309 is incremented by +1 each time the OUT-END 112 is issued when the data transfer from each of the output buffers 64 and 65 to the image memory 51 ends. A register 312 is adapted to store the row length (the length of one row) of the scale-converted image conversion in terms of words. A comparator 311 is adapted to compare the contents of the Y address register 309 and the register 312. Upon coincidence, a coincidence signal 358' is produced from the comparator 311 to increment the contents of the X address registers 313 and 314 by +1 and to decrement the contents of a row counter 310 by -1. The row counter 310 is initialized to the number of rows in the image subject to image scale conversion. When the contents of the row counter 310 reaches zero, indicating that the image scale conversion processing comes to an end, a data process end signal (DONE) 113 is sent to the system controller 54. The operational principle of the output controller 57 has been described thus far.

Turning now to FIG. 14, construction and operation of the saturation calculators (processing elements) 62 and 63 will be described. The saturation calculators 62 and 63 have the same construction and the following description will be given of the calculator 62 alone. The saturation calculator 62 functions to convert the image scale of the original image element data stored in the input buffers 58 and 59 and to store the data subject to the image scale conversion in an SP register (SP₁) 411. When receiving a PS-LOAD signal 106 from the system controller 54, the saturation calculator 62 loads the contents of the input buffers 58 and 59 on PS registers (PS₁₁ and PS₁₂) 401 and 402, respectively. The PS₁₁ 401 and PS₁₂ 402 are parallel/serial conversion shift registers which sequentially shift their contents in response to a clock signal φ₁ 114 fed from the shift controller 56 and deliver the contents to serial buffers (SB₁₁ and SB₁₂) 405 and 406, respectively. The SB₁₁ 405 and SB₁₂ 406 are shift registers which store image element data for two image elements and accordingly for four adjacent image elements in total. Assuming now that at a certain time, an image element Q_(mn) undergoes saturation calculation by an information processor (IP₁) 409, the shift controller 56 sends repeatedly a signal φ₁ 114 by a frequency which is required for loading four image elements of a reference frame C_(mn) for the Q_(mn) (namely, P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁) on the SB₁₁ 405 and SB₁₂ 406, as will be described later. When the four image elements in the SB₁₁ and SB₁₂ coincide with the reference frame for the Q_(mn), the shift controller 56 starts to send a clock signal φ₂ 115 to the image processor 409. Concurrently, the shift controller 56 also sends a vertical coordinate u_(m) (RA) 116 and a horizontal coordinate v_(m) (CA) 117 representative of the intramatrix coordinates of the Q_(mn). The information processor 409 utilizes data of the RA 116, CA 117, SB₁₁ 405 and SB₁₂ 406 to calculate the saturation. The manner of calculating the saturation involves known logical sum method, logical product/sum method and projection method (for example, Preliminary Transanctions for Image Engineering Conference, pp. 71 to 74, December 1981). The present invention is not concerned with an algorithm of the saturation calculation and the construction of the information processor 409 will not be described herein. Results of the saturation calculation for the Q_(mn) are sent from the information processor 409 at the timing of a clock signal φ₃ 118 to the SP₁ 411 for storage therein. The SP₁ 411 stores saturation calculation results for W image elements in an orderly manner without empty.

Referring now to FIG. 15, construction and operation of the shift controller 56 will be described. The shift controller 56 is started by a SHIFT-START signal 108 fed from the system controller 54. Upon receipt of the SHIFT-START signal 108, a clock gate 508 sends a clock to a clock generator 510 which generates three signals φ₁ 551, φ₂ 552 and φ₃ 553 of different phases as shown in FIG. 16. As has already been described, the original image element data set into the PS registers 401 to 404 in the saturation calculators 62 and 63 word by word is sequentially shifted so as to be loaded on the serial buffers 405 to 408. This shifting operation is driven by a signal φ₁ 114. Before the shift controller 56 is started by the SHIFT-START signal 108, the original image element data is stored in the PS registers 401 to 404 (FIG. 14) of the saturation calculators 62 and 63. However, since the serial bufers 405 to 408 are not provided with the original image element data at the first issuance of the SHIFT-START signal 108 after the commencement of the system start, it is necessary to transfer the data from each of the PS registers 401 to 404 to each of the serial buffers 405 to 408. The serial buffers 405 to 408 are two-bit shift registers and therefore, it will do that the signal φ₁ 114 is generated twice for the purpose of the data transfer from the PS registers 401 to 404. Accordingly, in FIG. 15, a skip counter 505 is initialized to a constant "2" prior to the commencement of the system start. The contents of the skip counter 505 is checked by a zero detector 506. If the contents are not zero, an AND gate 511 is enabled to send the signal φ₁ 114 in synchronism with the signal φ₁ 551. The signal φ₁ 114 shifts the contents of the PS registers 401 to 404 and serial buffers 405 to 408 by one bit and at the same time decrements the content of the skip counter 505 by -1. Since this operation is repeated until the content of the skip counter 505 becomes zero, data representative of initial two image elements is eventually transferred from the PS registers 401 to 404 to the serial buffers 405 to 408. When the contents of the skip counter 505 reaches zero, an AND gate 512 is enabled to set a FF 513 at the timing of the signal φ₁ 551. When the FF 513 is set, AND gates 514 and 515 are respectively enabled to send the signal φ₂ 115 and the signal φ₃ 118 in synchronism with the signal φ₂ 552 and the signal φ₃ 553, respectively. In response to the signal φ₂ 115, a heading data of a ΔY register 504 is loaded on the skip counter 505. The ΔY register 504 is thus a circulating register for storing the fundamental cycle for the periodic sequences of data representative of differences in the column numbers of the corresponding two original matrix points in the adjacent reference frames in the row direction, {ΔY₁, ΔY₂, . . . , ΔY_(s) }. Initially, the ΔY register 504 has a heading data of ΔY₁ which is loaded on the skip counter 505. Subsequently, the signal φ₃ 118 shifts the ΔY register 504 to update its contents to {ΔY₂, ΔY₃, . . . , ΔY_(s), ΔY₁ }. When receiving the signal φ₂ 115, the saturation calculators 62 and 63 calculate data representative of saturation levels for converted matrix points on the basis of the data of the serial buffers 405 to 408, vertical coordinates RA 116 and horizontal coordinates CA 117. Thereafter, upon receipt of the signal φ₃ 118, the saturation calculators 62 and 63 send the results of the saturation calculation to the SP registers 411 and 412 for storage therein. The signal φ₃ 118 resets the FF 513, shifts the ΔY register 504 and a v-register 517, and increments a column counter 503 by +1. The v-register 517 is a shift register for storing a fundamental cycle for the periodic sequence of data . representative of the horizontal coordinates {v₁, v₂, . . . , v_(s) }, and it sends its heading data, as the CA 117, to the saturation calculators 62 and 63. A column register 501 is adapted to store the row length (the length of one column) of the scale-converted image in terms of image elements. A comparator 502 is adapted to compare the content of the column register 501 with the content of the column counter 503. When coincident, the comparator 502 produces a coincidence signal which drives circulative shifting of content of a u-register 516 and resets the column counter 503. The u-register 516 is a shift register for storing a fundamental cycle for the periodic sequence of data representative of the vertical coordinates {u₁, u₂, . . . , u.sub. r }, and it sends its heading data, as the RA 116, to the saturation counters 62 and 63. The content of the u-register 516 is initially equal to {u₁, u₂, . . . , u_(r) } but circulated through {u₂, u₃, . . . , u_(r), u₁ }, {u₃, u₄, . . . , u_(r), u₁, u₂ } and so on as the shifting operation proceeds.

As will be seen from the foregoing description, the intra-matrix coordinates data necessary for the saturation calculation is provided by making reference to the contents of the circulating registers in contrast to the repetitions calculation for each individual image element pursuant to the conventional system and besides, the plurality of saturation counters make reference to the intra-matrix coordinates data in common to carry out the parallel processing.

The signal φ₁ 114 shifts the contents of the PS registers 401 to 404 and serial buffers 405 to 408, and the signal φ₃ 118 shifts the contents of the SP registers 411 and 412, as described previously. The PS registers 401 to 404 and the SP registers 411 and 412 are W-bit registers. Accordingly, by frequency dividing the signal φ₁ 114 and the signal φ₃ 118 by means of 1/W frequency dividers 507 and 509, respectively, a data empty signal (PS-EMPT) 107 for the PS registers 401 to 404 and a data full signal (SP-FULL) 109 for the SP registers 411 and 412 can be obtained. When either the PS-EMPT 107 or the SP-FULL 109 is sent to the system controller 54, the clock gate 508 is closed and the shift controller finishes operating.

Finally, construction and operation of the system controller 54 will be described by referencing FIG. 17. The system controller 54 is started by a SYS-START signal 102 fed from the processor 52. When the SYS-START signal 102 sets a FF 601, an AND gate 603 is enabled through an OR gate 602 and an IN-START signal 104 is sent in synchronism with a fundamental clock (CLK) signal 651. The IN-START signal 104 resets the FF 601 and a FF 604 and at the same time, sets a FF 605 which indicates that the input controller has been started. The IN-START signal 104 requests the input controller 55 to effect data transfer from the image memory 51 to the input buffers 58 to 61. When the data transfer to the input buffers 58 to 61 ends, an IN-END signal 105 is fed from the input controller 55 The IN-END signal 105 resets the FF 605 indicative of the operation of the input controller 55 in progress and sets a FF 606 indicative of data input end. On the other hand, a FF 607 is initially set. Accordingly, when the FF 606 is set, an AND gate 609 is enabled and a PS-LOAD signal 106 is sent in synchronism with the clock signal (CLK) 651. Thus, following the termination of the data transfer to the input buffers 58 to 61, the PS-LOAD signal 106 is sent. By this, the PS registers 401 to 404 included in the saturation counters 62 and 63, which registers are initially supplied with no original image element data, can conveniently be loaded with the data from the input buffers 58 to 61. The PS-LOAD signal 106 sets a FF 612 through an OR gate 611 so that an AND gate is enabled and a SHIFT-START signal 108 is sent to the shift controller 56 in synchronism with the CLK 651. The PS-LOAD signal 106 also resets FFs 610 and 606 and sets FFs 607 and 604. With the FF 604 set, the AND gate 603 is enabled through the OR gate 602 (since at this time a condition that neither data input nor data output is in progress must be held, the AND gate 603 can be opened only when the FF 605 and a FF 619 are reset), and the IN-START signal 104 is sent. Thus, concurrently with the transmission of the PS-LOAD signal 106, the data transfer to the input buffers 58 to 61 is started by the IN-START signal 104 and the saturation calculators are started by the SHIFT-START signal 108. The PS-LOAD signal 106 is issued not only when the system controller 54 receives, initially after the system start, a first IN-END signal 105 fed from the input controller 55 but also when the system controller 54 receives the PS-EMPT signal 107 fed from the shift controller 56. When the PS registers 401 to 404 in the saturation counters 62 and 63 empty of data, the PS-EMPT signal 107 indicative of the data empty is issued for loading data from the input buffers 58 to 61 on the PS registers 401 to 404. Conversely, when the SP registers 411 and 412 in the processing elements 62 and 63 are full of data, the shift controller 56 issues an SP-FULL signal 109 and this SP-FULL signal drives a FF 614 and an AND gate 615 to cause an OB-LOAD signal 110 to issue. Data in the SP registers 411 and 412 is read in response to the OB-LOAD signal 110 and written in the output buffers 64 and 65. The OB-LOAD signal 110 resets the FF 614 and at the same time, drives the OR gate 611, FF 612 and AND gate 613 so as to issue the SHIFT-START signal 108. The OB-LOAD signal 110 also drives a FF 617 and an AND gate 618 so as to issue an OUT-START signal 111. The OUT-START signal 111 starts data transfer from the output buffers 64 and 65 to the image memory 51. When the data transfer ends, the output controller 57 issues an OUT-END signal 112. The OUT-END signal 112 resets FF 616 and the FF 619 which indicates the operation of output controller 57 in progress. When receiving a DONE signal 113 fed from the output controller 57, the system controller 54 sends a SYS-END signal 103 to the processor 52.

As has been described, the present embodiment is advantageous in the following points:

(1) For obtaining data values for four original matrix points constituting a reference frame and intramatrix coordinates data necessary for the saturation calculation of the image subject to image scale conversion, the prior art apparatus needs coordinates calculation in respect of all the image elements whereas in the present embodiment reference is made to the fundamental cycle data, i.e., calculated values in tabular form {u₁, u₂, . . . , u_(r) }, {v₁, v₂, . . . , v_(s) }, {ΔX₁, ΔX₂, . . . , ΔX_(r) } and {ΔY₁, ΔY₂, . . . , ΔY_(s) }. Accordingly, the apparatus can be simplified and the image scale conversion processing can be carried out at high speeds.

(2) The parallel processing may be accomplished by using a plurality of saturation counters or processing elements, and the principal controllings including controlling of execution of the processing elements (namely, transmission and updating of the intra-matrix coordinates data and shift control of the image element data) and controlling of read/write addresses of the image memory can be carried out in common. Accordingly, the apparatus can be simplified and the image scale conversion processing can be carried out at high speeds. 

We claim:
 1. A method of converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and rod direction scales, said first and second two-dimensional images being of image elements arranged in first and second matrices respectively, the ratios between said first and second scales being predetermined column direction and row direction scale factors, respectively, comprising:first step of preparing at least one data sequence of fundamental cycle representing differences between those column order numbers in said first matrix which are particularly related to coordinates of image elements in said second matrix and those column order numbers in said first matrix which are particularly related to coordinates of image elements adjacent to the first-mentioned image elements in said second matrix; second step of selecting at least one row of image elements in said first matrix; third step of selecting sequentially at least one of the image elements in said first matrix within said selected row by the use of said prepared data sequence; and fourth step of determining sequentially a data value for each of the image elements on one row in said second matrix on the basis of the value for said selected at least one image element.
 2. A method according to claim 1, in which:at least two rows of image elements are selected in said second step; at least one image element is selected within each of said selected at least two rows; and the value for each of the image elements on one row in said second matrix is determined on the basis of the values for said selected image elements in said first matrix.
 3. A method according to claim 1, in which said first step includes dividing said column direction and row direction scales by first and second positive integers to define coordinates positions on said first image, said coordinate positions being determined in correspondence with each of said second image elements.
 4. A method according to claim 1, in which said data sequences is prepared in shift register means so as to use said data sequence repeatedly.
 5. An apparatus for converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and row direction scales, said first and second two-dimensional images being of image elements arranged in first and second matrices, respectively, the ratios between said first and second scales being predetermined column direction and row direction scales factors, respectively, comprising:means for preparing at least one data sequence of fundamental cycle representing differences between those column order numbers in said first matrix which are particularly related to coordinates of image elements in said second matrix and those column order numbers in said first matrix which are particularly related to coordinates of image elements adjacent to the first-mentioned image elements in aid second matrix; means for selecting at least one row of image elements in said first matrix; means for selecting sequentially at least one of the image elements in said first matrix within said selected row by the use of said prepared data sequence; and means for determining sequentially a data value for each of the image elements on one row in said second matrix on the basis of the value for said selected at least one image element.
 6. A method of converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and row direction scales, said first and second two-dimensional images being of image elements arranged in first and second matrices, respectively, the ratios between said first and second scales being predetermined column direction and row direction scale factors, respectively, comprising the steps of:determining, on the basis of the ratio between said first and second row direction scales, at least one data sequence for a first fundamental cycle for row direction periodic sequences of data, which first fundamental cycle of data defines the positional relation between the position on said first image corresponding to nay one of said second image elements and four first elements lying on the intersections between two adjacent rows and two adjacent columns in said first image elements matrix surrounding the position of said one second image element on said first image, said four first image elements constituting a reference frame for said one second image element; selecting two of the row in said first matrix; determining a reference frame for each of said second image elements from the image elements on said selected two rows in the first matrix and on the basis of said data sequences for said first fundamental cycles; producing at least one of the vertical and horizontal coordinates for each of said second image elements within its associated reference frame on the basis of said ratios between said first scales and second scales; and determining a data value for each of said second image elements the basis of the data value for at least one of the four first image elements of its associated reference frame and at least one of said vertical and horizontal coordinates of the position on said first image corresponding to the said second image element.
 7. A method according to claim 6, in which said step of producing the coordinates of said second image elements includes:determining, on the basis of said ratios between said first and second scales, at least one data sequence for a second fundamental cycle for at least one of vertical and horizontal periodic sequences of data, which second fundamental cycle of data defines the coordinates of the positions on said first image corresponding to said second image elements; and determining the coordinates for each of said second image elements within its associated reference frame on the basis of said data sequence for said second fundamental cycle.
 8. A method according to claim 6, in which said at least one data sequence for said first fundamental cycle for the row direction periodic sequence of data defines the difference in column number between one first image element in the reference frame for one of said second image elements and that first image element in the reference frame for the adjacent second image element in the row direction which lies on the same row as said one first image element in the reference frame for said one second image element.
 9. A method according to claim 8, further comprising the steps of:determining a first positive integer such that the product of said first positive integer and said ratio between said first and second column direction scales for said first and second image matrices constitutes a column side division factor (r) which is equal to a positive integer not less than 2, and determining a second positive integer such that the product of said second positive integer and said ratio between the row direction scales for said first and second image matrices constitutes a row side division factor (s) which is equal to a positive integer not less than 2; and dividing each of said reference frames in said first image element matrix into a (r×s) sub-matrix where the column and row sides of said each reference frame are divided by r and s, respectively, so that said second image elements lie on different intersections in said sub-matrices; whereby the period said second fundamental cycle for the column direction periodic sequences of data is identical with r or r divided by an integer while the period for each of said first and second fundamental cycles for the row direction periodic sequences of data is identical with s or s divided by an integer.
 10. An apparatus for converting a first two-dimensional image on first column direction and row direction scales and row direction scales, each of said first and second two-dimensional image being of image elements arranged in matrix, in which the position on said first image corresponding to each of said second image elements is associated with a reference frame constituted by four first image elements lying on the intersections of two adjacent rows and two adjacent columns in the first image element matrix surrounding said second image elements, the apparatus comprising:means for producing at least one data sequence for a first fundamental cycle for row direction periodic sequences of data as determined on the basis of the ratio between said first and second row direction scales, which first fundamental cycle of data defines the positional relation between said second image elements and their associated reference frames in said first image element matrix; means for selecting two rows of image elements data in said first matrix; means for storing said selected two rows of image element data; means coupled with said data sequence producing means for determining a reference frame for each of said second image elements from said stored image element data; means for producing the vertical and horizontal coordinates for each of said second image elements within its associated reference frame, said coordinates having a predetermined relationship with said ratio between said first and second scales; and means coupled with said reference frame determining means and with said coordinates producing means for determining a data value for each of said second image elements.
 11. An apparatus according to claim 10, in which said coordinates producing means includes means for producing data sequences for second fundamental cycles for vertical and horizontal periodic sequences of data determined on the basis of said ratio between said first and second scales, which second fundamental cycles of data define said coordinates for said second image elements and means coupled with said data sequence for said second fundamental cycles producing means for determining said coordinates.
 12. An apparatus according to claim 11, in which the product of a first positive integer and said ratio between said first and second column direction scales for said first and second image element matrices constitutes a column side division factor (r) which is equal to a positive integer not less than 2, and the product of a second positive integer and said ratio between said first and second row direction scales for said first and second image element matrices constitutes a row side division factor (s) which is equal to a positive integer not less than 2, so that the period for said second fundamental cycle for the vertical periodic sequences of data is equal to r or r divided by an integer, while the period for each of said first and second fundamental cycles for the horizontal periodic sequences of data are equal to s or s divided by an integer.
 13. An apparatus according to claim 10, in which said at least one data sequence for said first fundamental cycle for the row direction periodic sequence of data defines the differences in column number between one first image element in the reference frame for one of said second image elements and that first image element in the reference frame for the adjacent second image element in the row direction which lies on the same rows as said one first image element in the reference frame for said one second image element.
 14. An apparatus according to claim 13, in which the product of a first positive integer and said ratio between said first and second column direction scales for said first and second image element matrices constitutes a column side division factor (r) which is equal to a positive integer not less than 2, and the product of a second positive integer and said ratio between said first and second row direction scales for said first and second image element matrices constitutes a row side division factor (s) which is equal to a positive integer not less than 2, so that the period for said second fundamental cycle for the vertical sequences of data is equal to r or r divided by an integer, while the period for each of said first and second fundamental cycles for the horizontal periodic sequences of data are equal to s or s divided by an integer.
 15. An image scale converting apparatus for converting a first two-dimensional image to a second two-dimensional image, said first and second two-dimensional images being of image elements arranged in first and second matrices respectively, comprising: a buffer memory for storing a plurality of lines of image element data of said first two-dimensional image a first controller for controlling inputs to said buffer memory; a second controller for controlling shifting operation of said buffer memory; interpolation calculator means connected to receive data from said buffer memory for providing data values representative of the saturation level if image elements of said second two-dimensional image subjected to image scale conversion; and a plurality of circulating registers for storing interpolating address information to be supplied to said first and second controllers and said interpolation calculator means, one of said circulating registers storing at least one data sequence of fundamental cycle which represents a difference between those column order numbers in said first matrix which are particularly related to coordinates of image elements in said second matrix and those column order numbers in said first matrix which are particularly related to coordinates of image elements adjacent to the first-mentioned image elements in said second matrix, and said second controller including means for controlling said shifting operation of said buffer memory on the basis of the output of said circulating register.
 16. A method of enlarging or reducing a first two-dimensional image of image elements arranged in matrix with predetermined column direction and row direction scale factors to form a second two-dimensional image of image elements arranged in matrix, where an image element at the intersection between i-th row and j-th column in the matrix for said first image is represented by P_(ij), an image element at the intersection between m-th row and n-th column in the matrix for said second image and surrounded by four first image elements P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ is represented by Qmn, and the vertical and horizontal coordinates of said second image element within the rectangular region defined by said four first image elements are represented by u_(m) and v_(n), respectively, the method comprising:preparing data sequences for fundamental cycles for periodic sequences of data u_(m), v_(n) and ΔY_(n) =Y_(n+1) -Y_(n) determined on the basis of stored scale factors; selecting at least a pair of m-th and (m+1)-th rows of image elements in the first image matrix; selecting four first image elements within said selected rows by referring to said data sequences for said fundamental cycle of data ΔY_(n) ; determining said coordinates u_(m) and v_(n) of each of said second image elements by referring to said data sequences for said fundamental cycles; and determining a data value for each of said second image elements by use of the values of said selected four first image elements and said determined coordinates U_(m) and V_(n).
 17. A method according to claim 16, in which said image element selecting step is carried out simultaneously for those plural pairs of rows which include m-th and (m+kL)-th rows (k=1, 2, . . . ) where L is an integral number times the period of the fundamental cycle for a periodic sequence of data ΔX_(m) =x_(m+1) -X_(m) thereby to determine data values simultaneously for those second image elements which are on the same columns in different rows.
 18. An apparatus for enlarging or reducing a first two-dimensional image of image elements arranged in matrix with predetermined column direction and row direction scale factors to form a second two-dimensional image of image elements arranged in matrix, where an image element at the intersection between i-th row and j-th column in the matrix for said first image is represented by P_(ij), an image element at the intersection between m-th row and n-th column in the matrix for said second image and surrounded by four first image elements P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁ is represented by Q_(mn), and the vertical and horizontal coordinates of said second image element within the rectangular region defined by said four first image elements are represented by u_(m) and v_(n), respectively, the apparatus comprising:means for storing data sequences for fundamental cycles for periodic sequences of data u_(m), v_(n) and ΔY_(n) =Y_(n+1) -Y_(n) determined on the basis of said scale factors; means for selecting at least a pair of m-th and (m+1)-th rows of image elements in said first image matrix; means for selecting four first image elements within said selected rows by referring to said data sequences for said fundamental cycles of data ΔY_(n) ; means for determining said coordinates u_(m) and v_(n) of each of said second image elements by referring to said data sequences for said fundamental cycles; and means for determining a data value for each of said second image elements by use of the values of said selected four first image elements and said determined coordinates u_(m) and v_(m).
 19. An apparatus for enlarging or reducing a first two-dimension image of image elements arranged in a matrix with predetermined column direction and row direction scale factors to form a second two-dimensional image of image elements arranged in a matrix, where an image element at the intersection between the i-th row and j-th column in the matrix for said first image is represented by P_(ij), an image element at the interseciton between the m-th row and the n-th column in the matrix for said second image and surrounded by four first image elements P_(X).sbsb.m_(Y).sbsb.n, P_(X).sbsb.m_(+1Y).sbsb.n, P_(X).sbsb.m_(Y).sbsb.n₊₁ and P_(X).sbsb.m_(+1Y).sbsb.n₊₁) by Q_(mn), and the vertical and horizontal coordinates of said second image element within the rectangular region defined by aid four first image elements are represented by u_(m) and v_(n), respectively, the apparatus comprising:first means for storing image element data of said first image; second means for previously storing at least one data sequence for a fundamental cycle for periodic sequences of data ΔY_(n) =Y_(n+1) -Y_(n) ; third means for coupled to said first means for reading out at least one row of image element data; fourth means for selecting image element data, identified by addresses updated by said data sequence for said fundamental cycle of data ΔY_(n), within said read out image element data and for temporarily storing selected data; fifth means for previously storing data sequences for fundamental cycles for periodic sequences of data of said vertical and/or horizontal coordinates u_(m) and v_(n) ; and sixth means coupled to said fourth and fifth means for determining data values for said second image elements on the basis of said data sequences for said fundamental cycles for said vertical and horizontal coordinates data u_(m) and v_(n) successively read out from said fifth means and said element data successively selected within said read out image element data.
 20. A method of converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and row direction scales, said first and second two-dimensional images being of image elements arranged in first and second matrices, respectively, the ratios between said first and second scales being predetermined column direction and row direction scale factors, respectively, comprising:first step of preparing in memory means a data sequence representing differences between those column order numbers in said first image matrix which are placed in particular relation with mutually adjacent second image elements through mapping of a plurality of second image elements contained in one row in said second image matrix onto said first image matrix according to said row direction scale factor; second step of selecting at least one row in said first image matrix; third step of selecting at least one image element within of image elements contained in said selected at least one row by the use of said data sequence prepared in said memory means; and fourth step of determining a data value for one second image element on the basis of the value of said selected at least one image element in said first image matrix; said third and fourth steps being repeated to determine the values for the second image elements on one row in said second matrix related to said selected one row in said first matrix.
 21. A method according to claim 20, in which at least two image elements are selected in said third step, and the data value for one second image element is determined on the basis of the values of said selected plurality of image elements in said first matrix in said fourth step.
 22. A method according to claim 20, in which a plurality of rows are selected simultaneously in said first matrix in said second step, at least one image element is selected within each of said selected row by the use of said data sequence in said third step, and the data value for one second image element is determined on the basis of the values of said selected plurality of image elements in said first matrix in said fourth step.
 23. A method according to claim 20, in which said data sequence prepared in said memory means is constituted by at least one data sequence for a fundamental cycle for periodic sequences of data representing said differences between column order numbers.
 24. A method according to claim 20, further comprising the step of preparing in said memory means data sequences for defining a periodic positional relation between the position on said first image corresponding to any one of said second image elements and the position of at least one of said first elements adjacent to said one second image element on said first image, wherein said determination of the value for said second image element in said fourth step is carried out by the use of said prepared data sequence for defining said periodic positional relation.
 25. An apparatus for converting a first two-dimensional image on first column direction and row direction scales to a second two-dimensional image on second column direction and row direction scales, said first and second two-dimensional images being of image elements arranged in first and second matrices, respectively, the ratios between said first and second scales being predetermined column direction and row direction scale factors, respectively, comprising:means for preparing in memory means a data sequence representing differences between those column order numbers in said first image matrix which are placed in a particular relation with mutually adjacent second image elements through mapping of a plurality of second image elements contained in one said in said second image matrix onto said first image matrix according to said row direction scale factor; means for selecting at least one row in said first image matrix; means for selecting sequentially at least one image element within a plurality of image elements contained in said selected at least one row by the use of said data sequence prepared in said memory means; and means for determining sequentially a data value for each of the second image elements on one row in said second matrix on the basis of the value of said selected at least one image element in said first image matrix.
 26. An apparatus according to claim 25, in which said image element selecting means selected at least two image elements, and said data value determining means determines said data value for one second image element on the basis of the values of said selected plurality of image elements in said first matrix.
 27. An apparatus according to claim 25, in which said row selecting means selects a plurality of rows simultaneously in said first matrix, at least one image element is selected within each of said selected row by the use of said data sequence, and said data value determining means determines said data value for one second image element on the basis of the values of said selected plurality of image elements in said first matrix.
 28. An apparatus according to claim 25, in which said data sequence prepared in said memory means is one fundamental cycle for periodic sequence of data representing said difference between column order numbers. 